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Thermal Engineering: Optimization of an Industrial Furnace

In: An Introduction to Scientific Computing

Author

Listed:
  • Ionut Danaila

    (Université de Rouen Normandie, CNRS, Laboratoire de mathématiques Raphaël Salem)

  • Pascal Joly

    (Laboratoire Jacques-Louis Lions)

  • Sidi Mahmoud Kaber

    (Sorbonne Université, CNRS, Université Paris Cité, Laboratoire Jacques-Louis Lions)

  • Marie Postel

    (Sorbonne Université, CNRS, Université Paris Cité, Laboratoire Jacques-Louis Lions)

Abstract

In this chapter, we deal with a simple but realistic optimization problem. We have to find the optimal temperature in an industrial furnace, used to form resin pieces, such as car bumpers. The heating system is based on electric resistances, and the first part of this study is to compute the temperature field inside the oven when the values of the resistances are known. This step is called the direct problem: the resistances’ values are known and the temperature field is unknown. The second part of the study is devoted to computing the resistances’ values in order to maintain the bumper temperature at a prescribed value. This optimization problem is called an inverse problem: the temperature is the input and the resistances values are the outputs. For the numerical implementation, we use 2D triangular finite elements.

Suggested Citation

  • Ionut Danaila & Pascal Joly & Sidi Mahmoud Kaber & Marie Postel, 2023. "Thermal Engineering: Optimization of an Industrial Furnace," Springer Books, in: An Introduction to Scientific Computing, edition 2, chapter 0, pages 309-325, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-35032-0_14
    DOI: 10.1007/978-3-031-35032-0_14
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